I never thought about the relationship between "ignore" and "ignorant". Maybe someone who is ignorant ignores information .

As for "owe," if you borrow money from someone and intend to pay them back, you owe them the amount. If they borrow from you and intend to pay you back, they owe you. The same kind of language is often used if someone does you a favor, for example. A common response is "Thanks, I owe you one."